RV-30-001 · Surd dimensions: exact perimeter, area and diagonal

A rectangle has sides

11\sqrt{5}

cm and

8\sqrt{5}

cm.

Diagram not accurately drawn

(a) Find its exact perimeter and area. Simplify your answers.

(b) Find the exact length of a diagonal.

Part (a) Surds in Geometry: Perimeter, Area & Pythagoras Diagonal Booklet p. 34 & p. 46

Method

1) Perimeter: add like surds

2) Area: multiply surds using a√s × b√s = ab × s

3) Diagonal: use Pythagoras d² = w² + l²

Worked Example (RV-30-001 · Part (a))

Find its exact perimeter and area. Simplify your answers.

Add like surds for the perimeter.

38\sqrt{5}

Multiply the two lengths; √s × √s = s.

440 cm²

Ans =

38\sqrt{5}

cm; 440 cm².

Part (b) Surds in Geometry: Perimeter, Area & Pythagoras Diagonal Booklet p. 34 & p. 46

Method

1) Perimeter: add like surds

2) Area: multiply surds using a√s × b√s = ab × s

3) Diagonal: use Pythagoras d² = w² + l²

Worked Example (RV-30-001 · Part (b))

Find the exact length of a diagonal.

Use Pythagoras with the exact squared side lengths.

\sqrt{925}

Ans =

\sqrt{925}